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by prachi18oct » Mon Jun 22, 2015 11:25 am
30 people in total attended an office party for a colleague's birthday. The birthday cake was sliced into exactly 32 pieces, all of which were eaten. Did everyone who attended eat at least one slice of cake?

(1) One person ate exactly 2 slices of cake.

(2) One person ate exactly 3 slices of cake.

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.
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Source: — Data Sufficiency |
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by Ian Stewart » Mon Jun 22, 2015 11:33 am
Neither statement is sufficient alone - looking at S2, for example, if one person eats exactly 3 slices, then there are 29 slices left, and 29 people left. So it's certainly possible that everyone had one slice, but we have no way to know for sure.

When we use both statements, we know that 5 slices were eaten by 2 people. So we have 27 slices left, and 28 people left, and there just aren't enough slices to go around. So using both statements, we know the answer to the question must be 'no', and the answer is C.
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by [email protected] » Mon Jun 22, 2015 4:53 pm
Hi prachi18oct,

In these types of questions, you have to pay careful attention to what you KNOW and what you DON'T KNOW. For example, in this prompt there are no restrictions on the number of pieces of cake that any one person could have eaten. 1 person could have potentially eaten ALL of the slices. THAT possibility impacts all of the steps that follow. It's also possible that 2 people ate 3 of the slices (1.5 slices for each).

We're told that there are 30 people and 32 slices of cake (and that all slices were eaten). The question asks if each person ate at least one slice of cake. This is a YES/NO question.

Fact 1: 1 person ate 2 slices.

That leaves 29 people and 30 slices of cake.
It IS possible that everyone ate a slice of cake (and the answer is YES)
It IS possible that 1 person ate the rest of the cake (and the answer is NO).
Fact 1 is INSUFFICIENT

Fact 2: 1 person ate 3 slices.

That leaves 29 people and 29 slices of cake.
It IS possible that everyone ate a slice of cake (and the answer is YES)
It IS possible that 1 person ate the rest of the cake (and the answer is NO)
Fact 2 is INSUFFICIENT

Combined, we know...
1 person ate 2 slices
1 person ate 3 slices

That leaves 28 people and 27 slices of cake.
It is NOT POSSIBLE that everyone ate a slice of cake (and the answer is ALWAYS NO).
Combined, SUFFICIENT

Final Answer: C

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by Jeff@TargetTestPrep » Thu Dec 07, 2017 7:14 am
prachi18oct wrote:30 people in total attended an office party for a colleague's birthday. The birthday cake was sliced into exactly 32 pieces, all of which were eaten. Did everyone who attended eat at least one slice of cake?

(1) One person ate exactly 2 slices of cake.

(2) One person ate exactly 3 slices of cake.
We are given that a total of 30 people attended a party and ate a total of 32 slices of cake. We need to determine whether everyone ate at least one slice.

Statement One Alone:

One person ate exactly 2 slices of cake.

Since one person ate exactly 2 slices of cake, the remaining 29 people ate a total of 30 slices of cake. However, we cannot determine whether everyone ate at least one slice of cake.

It's possible that 28 of the remaining 29 people each ate exactly 1 slice of cake and the 29th person ate 2 slices of cake. However, it's also possible that 27 of the remaining 29 people each ate exactly 1 slice of cake, the 28th person ate 3 slices of cake, and the 29th person did not eat a slice of cake.

Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

One person ate exactly 3 slices of cake.

Since 1 person ate exactly 3 slices of cake, the remaining 29 people ate a total of 29 slices of cake. However, we cannot determine whether everyone ate at least one slice of cake.

It's possible that the remaining 29 people each ate exactly 1 slice of cake. However, it's also possible that 27 of the remaining 29 people each ate exactly 1 slice of cake, the 28th person ate 2 slices of cake, and the 29th person did not eat a slice of cake.

Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

With the information given in the two statements, we know that the remaining 28 (30 - 1 - 1 = 28) people ate a total of 27 (32 - 2 - 3 = 27) slices of cake. Since there are more people than slices of cake, we can determine that not every person ate a slice of cake. The two statements together are sufficient to answer the question.

Answer: C

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Head of GMAT Instruction
[email protected]

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